Problem: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 3x + 1$ and $ BC = 9x - 41$ Find $AC$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {3x + 1} = {9x - 41}$ Solve for $x$ $ -6x = -42$ $ x = 7$ Substitute $7$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 3({7}) + 1$ $ BC = 9({7}) - 41$ $ AB = 21 + 1$ $ BC = 63 - 41$ $ AB = 22$ $ BC = 22$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {22} + {22}$ $ AC = 44$